Quantum computing device using two gate types to prevent frequency collisions in superconducting quantum computers

ABSTRACT

A quantum computing device including a first plurality of qubits having a first resonance frequency and a second qubit having a second resonance frequency, the second resonance frequency being different from the first resonance frequency; and a first tunable frequency bus configured to couple the first plurality of qubits to the second qubit.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support contractW911NF-14-1-0124 awarded by the Army Research Office (ARO). TheGovernment has certain rights to this invention.

BACKGROUND

The currently claimed embodiments of the present invention relate tosuperconducting quantum computers, and more specifically, tosuperconducting quantum computers that combine two gate types to avoidfrequency collisions.

Quantum computation is based on the reliable control of quantum bits(referred to herein throughout as qubits). The fundamental operationsrequired to realize quantum algorithms are a set of single-qubitoperations and two-qubit operations which establish correlations betweentwo separate quantum bits. The realization of high fidelity two-qubitoperations may be desirable both for reaching the error threshold forquantum computation and for reaching reliable quantum simulations.

Currently for superconducting qubits single-qubit gates are implementedwith microwave controls. There are three main types of two-qubit gates:gates based on tunable frequency qubits, gates based on microwave-drivenqubits (e.g., cross-resonance, flick fork, Bell Rabi, MAP, sidebandtransitions, and gates based on geometric phases (e.g.,resonator-induced phase gate, holonomic gates)).

For gates based on tunable frequency qubits, the qubits themselves aretuned in frequency to activate a resonance interaction. These gatesessentially have two operating points: an ‘off’-position withessentially zero coupling and an ‘on’ position when the qubits have astrong two-qubit interaction. These gates have a very good on-off ratio,but because the qubits are tunable via externally applied magnetic flux,they can be limited by 1/f noise which limits the coherence of thequbits to a few microseconds.

For gates based on microwave-driven qubits, the qubits can he designedto be fixed in frequency so they are immune to flux noise. However,microwave pulses are required to activate the gate. The problems withthese gates are that they have a low on/off ratio and are very hard toaddress the gate of interest without activating unwanted interactions.

Gates based on geometric phases are based on the path of the quantumstate in its state space and the acquired quantum phase associated withits excursion. Adiabatic geometric gates are robust against certaintypes of noise, but are generally slow and require controls toadiabatic. Non-adiabatic gates can be faster and potentially share thenoise-resilience of their adiabatic cousins.

Superconducting Josephson junction qubits are a promising technology forbuilding a quantum computer. The transmon-type of superconducting qubitsis operated at a relatively high ratio of Josephson energy to chargingenergy that allows the transmon (transmission-line shunted plasmaoscillation) qubit to operate at reduced charge noise sensitivity whilestill allowing coupling between qubits and between the qubits and thetransmission line or bus. This allows transmon qubits to be coupled in a2D arrangement with nearest neighbor interactions (for example in atwo-dimensional lattice) via fixed-frequency microwave resonators. Fixedfrequency transmon qubits (single-junction transmons) are highlycoherent (i.e., essentially having a single resonance frequency).Therefore, there is a need to enable interactions between qubits.Cross-Resonance (CR) interaction between qubits can be used to couplethe qubits. In Cross-Resonance, the qubits are driven with microwavetones at the frequency of the neighboring qubits to establishinteraction between the qubits. To enable CR interaction between aplurality of qubits, the qubits are relatively closely spaced infrequency (for example less than 200 MHz). However, this leads tofrequency collision issues and crosstalk between the qubits.

As future quantum computers may use a large number of qubits (hundredsto thousands, or more), it may be desirable to limit frequency collisionor crosstalk between qubits. While CR may provide benefits in allowingcoupling between neighboring qubits, CR may not be adequate forestablishing coupling between farther away located qubits. Hence, a needremains for a solution that cures the frequency collision issue andcrosstalk when using CR to couple qubits.

SUMMARY

An aspect of the present invention is to provide a quantum computingdevice including a first plurality of qubits having a first resonancefrequency and a second qubit having a second resonance frequency, thesecond resonance frequency being different from the first resonancefrequency. The quantum computing device also includes a first fixedfrequency bus configured to couple the first plurality of qubits, thefirst plurality of qubits being configured to interact viacross-resonance through the first fixed frequency bus. The quantumcomputing device further includes a first tunable frequency busconfigured to couple at least one of the first plurality of qubits tothe second qubit.

In an embodiment, the quantum computing device further includes a secondplurality of qubits having the second resonance frequency; and a secondfixed frequency bus configured to couple the second plurality of qubits,the second plurality of qubits being configured to interact viacross-resonance through the second fixed frequency bus. In anembodiment, the first plurality of qubits are arranged in one of a firstrow or in a first column and are configured to interact viacross-resonance through the first fixed frequency bus, and the secondplurality of qubits are arranged in one of a second row or in a secondcolumn and are configured to interact via cross-resonance through thesecond fixed frequency bus.

In an embodiment, the quantum computing device further includes a thirdplurality of qubits having the first resonance frequency, the thirdplurality of qubits being arranged in one of a third row or in a thirdcolumn; and a third fixed frequency bus configured to couple the thirdplurality of qubits, the third plurality of qubits being configured tointeract via cross-resonance through the third fixed frequency bus.

In an embodiment, the first plurality of qubits arranged in the firstrow or in the first column are configured to interact with the secondplurality of qubits arranged in the second row or the second column viathe first tunable frequency bus and the second plurality of qubitsarranged in the second row or in the second column are configured tointeract with the third plurality of qubits arranged in the third row orthe third column via the first tunable frequency bus. In an embodiment,the second plurality of qubits are arranged between the first pluralityof qubits and the third plurality of qubits so as to preventcross-resonance interaction between the first plurality of qubits andthe third plurality of qubits.

In an embodiment, the quantum computing device further includes a thirdplurality of qubits having a third resonance frequency, the thirdplurality of qubits being arranged in one of a third row or in a thirdcolumn, the third resonance frequency being different from the firstresonance frequency and different from the second resonance frequency; athird fixed frequency bus configured to couple the third plurality ofqubits, the third plurality of qubits being configured to interact viacross-resonance through the third fixed frequency bus; and a secondtunable frequency bus configured to couple at least one of the thirdplurality of qubits to the second plurality of qubits.

In an embodiment, the first plurality of qubits arranged in the firstrow or in the first column are configured to interact with the secondplurality of qubits arranged in the second row or the second column viathe first tunable frequency bus, and the second plurality of qubitsarranged in the second row or in the second column are configured tointeract with the third plurality of qubits arranged in the third row orthe third column via the second tunable frequency bus.

Another aspect of the present invention is to provide another quantumcomputing device. The quantum computing device includes a firstplurality of qubits having a first resonance frequency and a secondqubit having a second resonance frequency, the second resonancefrequency being different from the first resonance frequency. Thequantum computing device further includes a first tunable frequency busconfigured to couple the first plurality of qubits to the second qubit.

In an embodiment, the first plurality of qubits are configured tointeract with each other through the first tunable frequency bus viacross-resonance. In an embodiment, at least one of the first pluralityof qubits and the second qubit are configured to interact through aparametric iSWAP gate.

In an embodiment, the first plurality of qubits comprise three qubits,the three qubits being configured to interact with each other throughthe first tunable frequency bus via cross-resonance, and the secondqubit being configured to interact with the three qubits through thefirst tunable frequency bus via a parametric iSWAP gate.

In an embodiment, the quantum computing device further includes a secondplurality of qubits having the second resonance frequency and a thirdqubit having the first resonance frequency; and a second tunablefrequency bus configured to couple the third qubit to the secondplurality of qubits. In an embodiment, the second plurality of qubitsare configured to interact with each other through the second tunablefrequency bus via cross-resonance. In an embodiment, the third qubit isprevented from interacting via cross-resonance with the first pluralityof qubits.

In an embodiment the quantum computing device further includes a secondplurality of qubits having the second resonance frequency and a thirdqubit having a third resonance frequency, the third resonance frequencybeing different from the first resonance frequency and the secondresonance frequency; and a second tunable frequency bus configured tocouple the third qubit to the second plurality of qubits.

Another aspect of the present invention is to provide a method ofproducing a quantum computing device. The method includes producing afirst plurality of qubits having a first resonance frequency and asecond qubit having a second resonance frequency on a qubit chip, thesecond frequency being different from the first frequency; at least oneof producing a first fixed frequency bus on the qubit chip or attachingthe qubit chip to a chip comprising the first frequency bus so as toenable interaction between the first plurality of qubits viacross-resonance; and at least one of producing a first tunable frequencybus on the qubit chip or attaching the qubit chip to a chip comprisingthe first tunable frequency bus so as to enable coupling at least one ofthe first plurality of qubits to the second qubit using the firsttunable frequency bus.

Yet another aspect of the present invention is to provide a method ofproducing a quantum computing device. The method includes producing afirst plurality of qubits having a first resonance frequency and asecond qubit having a second resonance frequency on a qubit chip, thesecond frequency being different from the first frequency; and at leastone of producing a first tunable frequency bus on the qubit chip orattaching the qubit chip to a chip comprising the first tunablefrequency bus so as to enable coupling at least one of the firstplurality of qubits to the second qubit using the first tunablefrequency bus.

The frequency of a qubit corresponds to the transition energy betweentwo states of the qubit being used, for example between the ground stateand the first excited state. A qubit has two quantum states (e.g.,ground state and first excited state) that are sufficiently separated inenergy to form separated energy levels and/or decoupled from anyadditional quantum states so that the qubit is approximately atwo-quantum state structure under operation conditions. The transitionenergy between the two states defines the resonance frequency of thequbit. For some qubits, the transition energy can be modified, forexample, by the application of a magnetic field.

The term “resonance frequency” of a qubit as used in this specificationcorresponds to the frequency resonant with the energy separation betweentwo energy levels of the qubit (e.g., ground state energy level andexcited state energy level). The resonance frequency defines the energytransition from one energy level to another energy level. Each “energylevel” of a qubit corresponds to an energy level defined within arelatively narrower bandwidth of energies or frequencies. The term“narrower” is used herein to mean that the bandwidth is smaller than thetransition energy between the energy states of the qubit. For example,the production of a plurality of qubits that are intended to have thesame resonance frequency may actually result in qubits with smalldifferences in resonance frequency, but still within the bandwidth.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure, as well as the methods of operation andfunctions of the related elements of structure and the combination ofparts and economies of manufacture, will become more apparent uponconsideration of the following description and the appended claims withreference to the accompanying drawings, all of which form a part of thisspecification, wherein like reference numerals designate correspondingparts in the various figures. It is to be expressly understood, however,that the drawings are for the purpose of illustration and descriptiononly and are not intended as a definition of the limits of theinvention.

FIG. 1 is a schematic diagram of a quantum computing device having aplurality of qubits, according to an embodiment of the presentinvention;

FIG. 2A is a schematic diagram of a quantum circuit including two qubitsinteracting via a first fixed frequency bus (CR bus), according to anembodiment of the present invention;

FIG. 2B is a schematic diagram of a quantum circuit including two qubitsinteracting via a first tunable frequency bus, according to anembodiment of the present invention;

FIG. 3 is a schematic diagram of a quantum computing device having aplurality of qubits, according to another embodiment of the presentinvention;

FIG. 4A shows a schematic diagram of a quantum circuit including fourqubits interacting via a first tunable frequency bus, according to anembodiment of the present invention;

FIG. 4B shows a schematic diagram of four qubits interacting via thefirst tunable frequency bus, according to embodiment of the presentinvention;

FIG. 4C is an image of a quantum computing device on a chip includingfour qubits and a tunable frequency bus, according to an embodiment ofthe present disclosure;

FIG. 5A is an energy diagram showing the first excited energy levels offour qubits Q₁, Q₂, Q₃ and Q₄, according to an embodiment of the presentinvention;

FIG. 5B is a plot of the energy or frequency of the first excited energylevels of the four qubits Q₁, Q₂, Q₃ and Q₄, according to an embodimentof the present invention; and

FIG. 6 is a plot of the population in qubit Q₃ as a function of thefrequency modulating the tunable bus versus time, in accordance with anembodiment of the present invention.

DETAILED DESCRIPTION

FIG. 1 is a schematic diagram of a quantum computing device having aplurality of qubits, according to an embodiment of the presentinvention. The quantum computing device 10 includes a first plurality ofqubits 12 having a first resonance frequency. The quantum computingdevice 10 further includes a second qubit or a second plurality ofqubits 14 having a second resonance frequency. The second resonancefrequency is different from the first resonance frequency. For example,the second resonance frequency of the second qubit or the secondplurality of qubits can be relatively higher than the first resonancefrequency of the first plurality of qubit. For example, the firstplurality of qubits may have a first resonance frequency in the range4.8-5.0 GHz and the second qubit or qubits may have a second resonancefrequency in the range 5.6-5.8 GHz.

Although four first qubits are shown in FIG. 1 , as it must beappreciated two or more qubits can be used. Similarly, although foursecond qubits are shown in FIG. 1 , as it must be appreciated one, twoor more second qubits can be used. However, in practicalimplementations, often more than two first qubits and more than twosecond qubits are used.

As shown in FIG. 1 , the quantum computing device 10 further includes afirst fixed frequency bus 16 (depicted as a dotted line) configured tocouple the first plurality of qubits 12. The first plurality of qubits12 are configured to interact via cross-resonance (CR) through the firstfixed frequency bus 16. The quantum computing device 10 further includesa first tunable frequency bus 18 configured to couple at least one ofthe first plurality of qubits 12 to a second qubit 14. In an embodiment,the first tunable frequency bus 18 is configured to couple the firstplurality of qubits 12 (for example four as shown in FIG. 1 ) to asecond plurality of qubits 14 (for example four as shown in FIG. 1 ). Inan embodiment, the first tunable frequency bus 18 is configured tocouple the at least one of the first plurality of qubits 12 and thesecond qubit 14 through a parametric iSWAP gate. In an embodiment, thefirst tunable frequency bus 18 is configured to couple the firstplurality of qubits 12 and the second plurality of qubits 14 through theparametric iSWAP gate.

In an embodiment, the quantum computing device 10 further includes asecond fixed frequency bus 17 configured to couple the second pluralityof qubits 14. The second plurality of qubits 14 are configured tointeract via cross-resonance (CR) through the second fixed frequency bus17.

FIG. 2A is a schematic diagram of a quantum circuit including two qubitsinteracting via the first fixed frequency bus (CR bus), according to anembodiment of the present invention. As shown in FIG. 2A, first qubit Q₁in the first plurality of qubits 12 and second qubit Q₂ in the firstplurality of qubits 12 interact via first fixed frequency bus 16 (CRbus). In an embodiment, the first fixed frequency bus 16 is a microwavetransmission line connecting qubit Q₁ to qubit Q₂. Similarly, althoughnot illustrated in FIG. 2A, first qubit Q₁ in the second plurality ofqubits 14 and second qubit Q₂ in the second plurality of qubits 14interact via second fixed frequency bus (CR bus) 17. In an embodiment,the second fixed frequency bus 17 is a microwave transmission lineconnecting qubit Q₁ to qubit Q₂. In the qubits Q₁ and Q₂, the verticallines “∥” correspond to a capacitance and the “X” symbol corresponds toa Josephson junction. Although the qubit is shown having a singleJosephson Junction (JJ) and a single capacitance, any number ofJosephson junctions and any number of capacitances can be used. Inaddition, other elements can also be included in the circuit of thequbits Q₁ and Q₂ and first fixed frequency bus 16 (CR bus) and/or secondfixed frequency bus 17 (CR bus).

FIG. 2B is a schematic diagram of a quantum circuit including two qubitsinteracting via the first tunable frequency bus 18, according to anembodiment of the present invention. As shown in FIG. 2B, first qubit Q₁in the first plurality of qubits 12 and second qubit Q₂ in the firstplurality of qubits 12 interact via first tunable frequency bus 18 (forexample via a parametric iSWAP gate). In an embodiment, as shown in FIG.2B, the first tunable frequency bus 18 includes a gate (e.g., aparametric iSWAP gate) “G” that connects qubit Q₁ to qubit Q₂ via atransmission line. The gate “G” is activated by applying a magneticfield “B”. Similar to FIG. 2A, in the qubits Q₁ and Q₂, the verticallines “∥” correspond to a capacitance and the “X” symbol corresponds toa Josephson junction. Although the qubits Q₁ and Q₂ are shown having asingle Josephson junction and a single capacitance, any number ofJosephson junctions and any number of capacitances can be used. Inaddition, other elements can also be included in the circuit of thequbits Q₁ and Q₂. In addition, although the first tunable frequency bus18 is shown having gate “G” (e.g., parametric iSWAP gate) using twoJosephson junctions, as it can be appreciated, other types of gates canbe used that use another number of Josephson junctions. In anembodiment, the first tunable frequency bus 18 includes asuperconducting quantum interference device (SQUID). The term parametriciSWAP gate is understood in the superconducting quantum computing art asbeing a gate that performs a swap in the phase matrix through theimaginary number “i”.

As shown in FIG. 1 , the first plurality of qubits 12 are arranged acolumn. However, the first plurality of qubits 12 can also be arrangedin a first row. The first plurality of qubits 12 are configured tointeract via cross-resonance (CR) through the first fixed frequency bus16. As also shown in FIG. 1 , the second plurality of qubits 14 arearranged in a second column. However, the second plurality of qubits 14can also be arranged in a second row. The second plurality of qubits 14are configured to interact via cross-resonance (CR) through the secondfixed frequency bus 17.

As also shown in FIG. 1 , in an embodiment, the quantum computing device10 also includes a third plurality of qubits 13 having the firstresonance frequency similar to the first plurality of qubits 12. Asshown in FIG. 1 , the third plurality of qubits 13 are arranged in athird column. However, the third plurality of qubits 13 can also bearranged in a third row. The quantum computing device further includes athird fixed frequency bus 19 configured to couple the third plurality ofqubits 13. The third plurality of qubits 13 are configured to interactvia cross-resonance (CR) through the third fixed frequency bus 19.

As also shown in FIG. 1 , in an embodiment, the quantum computing device10 also includes a fourth plurality of qubits 15 having the secondresonance frequency similar to the second plurality of qubits 14. Asshown in FIG. 1 , the fourth plurality of qubits 15 are arranged in afourth column. However, the fourth plurality of qubits 15 can also bearranged in a fourth row. The quantum computing device 10 furtherincludes a fourth fixed frequency bus 21 configured to couple the fourthplurality of qubits 15. The fourth plurality of qubits 15 are configuredto interact via cross-resonance (CR) through the fourth fixed frequencybus 21.

In an embodiment, the first plurality of qubits 12 arranged in the firstrow or in the first column are configured to interact with the secondplurality of qubits 14 arranged in the second row or the second columnvia the first tunable frequency bus 18. In an embodiment, the secondplurality of qubits 14 arranged in the second row or in the secondcolumn are configured to interact with the third plurality of qubits 13arranged in the third row or the third column via the first tunablefrequency bus 18. In an embodiment, the third plurality of qubits 13arranged in the third row or in the third column are configured tointeract with the fourth plurality of qubits 15 arranged in the fourthrow or the fourth column via the first tunable frequency bus 18.

In an embodiment, the second plurality of qubits 14 are arranged betweenthe first plurality of qubits 12 and the third plurality of qubits 13 soas to prevent cross-resonance interaction, and thus substantially reduceor eliminate frequency collision and crosstalk, between the firstplurality of qubits and the third plurality of qubits 13. Similarly, thethird plurality of qubits 13 are arranged between the second pluralityof qubits 14 and the fourth plurality of qubits 15 so as to preventcross-resonance interaction, and thus substantially reduce or eliminatefrequency collision and crosstalk, between the second plurality ofqubits 14 and the fourth plurality of qubits 15.

In an embodiment, the third plurality of qubits 13 have a thirdresonance frequency. The third plurality of qubits 13 are arranged in athird column, as shown in FIG. 1 . However, the third plurality ofqubits 13 can also be arranged in a third row. In this embodiment,however, the third resonance frequency is different from the firstresonance frequency of the first plurality of qubits 12 and differentfrom the second resonance frequency of the second plurality of qubits14. In an embodiment, the third fixed frequency bus 19 is configured tocouple the third plurality of qubits 13. The third plurality of qubits13 are configured to interact via cross-resonance (CR) through the thirdfixed frequency bus 19. In an embodiment, the quantum computing deviceincludes a second tunable frequency bus 22 that is configured to coupleat least one of the third plurality of qubits 13 to the second pluralityof qubits 14.

In an embodiment, the first plurality of qubits 12 arranged in the firstrow or in the first column are configured to interact with the secondplurality of qubits 14 arranged in the second row or the second columnvia the first tunable frequency bus 18. In an embodiment, the secondplurality of qubits 14 arranged in the second row or in the secondcolumn are configured to interact with the third plurality of qubits 13arranged in the third row or the third column via the second tunablefrequency bus 22.

In an embodiment, the first, the second, the third and/or fourthplurality of qubits can be transmon qubits.

FIG. 3 is a schematic diagram of a quantum computing device having aplurality of qubits, according to another embodiment of the presentinvention. The quantum computing device 30 includes a first plurality ofqubits 32 having a first resonance frequency and a second qubit 34having a second resonance frequency. The second resonance frequency isdifferent from the first resonance frequency. In an embodiment, thesecond frequency is higher than the first frequency, for example. In anembodiment, for example the second frequency can be in the range 4.8-5.0GHz and the first frequency can be in the range 5.6-5.8 GHz. The quantumcomputing device further includes a first tunable frequency bus 36configured to couple the first plurality of qubits 32 to the secondqubit 34.

In an embodiment, the first plurality of qubits 32 are configured tointeract with each other through the first tunable frequency bus 36 viacross-resonance (CR).

FIG. 4A shows a schematic diagram of a quantum circuit including fourqubits interacting via the first tunable frequency bus 36, according toan embodiment of the present invention. FIG. 4B shows a schematicdiagram of four qubits interacting via the first tunable frequency bus36, according to embodiment of the present invention. FIG. 4C is animage of a quantum computing device on a chip including four qubits anda tunable frequency bus, according to an embodiment of the presentdisclosure. As shown in FIG. 4A, qubits Q₁, Q₂ and Q₄ of the firstplurality of qubits 32 interact with each other and with the qubit Q₃corresponding to the second qubit 34 via the first tunable frequency bus36 (for example, via a parametric iSWAP gate).

In an embodiment, as shown in FIG. 4A, the first tunable frequency bus36 includes a gate (e.g., a parametric iSWAP gate) “G” that connectsqubits Q₁, Q₂, Q₃, and Q₄ using a transmission lines connected toquantum gate “G”. The gate “G” is activated by applying a magnetic field“B”. In the qubits Q₁, Q₂, Q₃, and Q₄ the vertical lines “∥” correspondto a capacitance and the “X” symbol corresponds to a Josephson junction.Although the qubits Q₁, Q₂, Q₃, and Q₄ are shown having a singleJosephson junction and a single capacitance, any number of Josephsonjunctions and any number of capacitances can be used. In addition, otherelements can also be included in the circuit of the qubits Q₁, Q₂, Q₃,and Q₄. In addition, although the first tunable frequency bus 36 isshown having gate “G” (e.g., parametric iSWAP gate) using two Josephsonjunctions, as it can be appreciated, other types of gates can be usedthat use another number of Josephson junctions. In an embodiment, thefirst tunable frequency bus 36 includes a superconducting quantuminterference device (SQUID). Therefore, in an embodiment, the firstplurality of qubits 32 and the second qubit 34 are configured tointeract the first tunable frequency bus 36 (via a parametric iSWAPgate).

In an embodiment, as shown in FIGS. 3, 4A and 4B, the first plurality ofqubits 32 comprise three qubits (for example, Q₁, Q₂ and Q₄). The threequbits 32 (Q₁, Q₂ and Q₄) are configured to interact with each otherthrough the first tunable frequency bus 36 via cross-resonance (CR). Thesecond qubit 34 (Q₃) is configured to interact with the three qubits 32(Q₁, Q₂ and Q₄) through the first tunable frequency bus 36 (via aparametric iSWAP gate).

FIG. 5A is an energy diagram showing the first excited energy levels ofthe four qubits Q₁, Q₂, Q₃ and Q₄, according to an embodiment of thepresent invention. The first excited energy level of qubit Q₁ is denotedas |0001>, the first excited energy level of qubit Q₂ is denoted as|0010>, the first excited energy level of qubit Q₄ is denoted as |1000>,and the first excited energy level of qubit Q₃ is denoted as |0100>. Thefrequencies noted above each excited energy state correspond to atransition energy (or frequency) between the ground state (energy orfrequency equal to zero) and the first excited energy level,respectively, 4.605 GHz for Q₁, 4.685 GHz for Q₂, 4.727 for Q₄ and 5.478for Q₃. As shown in FIG. 5A, the excited energy levels |0001>, |0010>and|1000>of qubits Q₁, Q₂, and Q₄, respectively, are close to each otherwith a difference in energy between |0001> and |0010> of 80 MHz, between|0010> and |1000> of 42 MHz, and between |0001> and |1000> of 122 MHz.This allows qubits Q₁, Q₂, and Q₄ to interact via CR. On the other hand,the difference in energy between the excited energy level |0100> ofqubit Q₃ and energy levels |0001> of qubit Q₁, between the excitedenergy level |0100> of qubit Q₃ and energy level |0010> of qubit Q₂ andbetween the excited energy level |0100> of qubit Q₃ and energy level|1000> of qubit Q₄ is, respectively, 873 MHz, 793 MHZ and 751 MHz. whichis greater than any of 80 MHz, 42 MHz and 122 MHz. As a result, in thiscase interaction between qubits Q₁, Q₂, Q₄ and Q₃ is enabled by thefirst tunable frequency bus 36 (using for example the parametric iSWAPgate). The inventors implemented a quantum computing device with thefour qubits Q₁, Q₂, Q₃ and Q₄ coupled to a tunable frequency bus using aparametric iSWAP gate. The inventor reported results that showsuccessful implementation of the interaction between the various qubits.The inventors plotted the results.

FIG. 6 is a plot of the population in qubit Q₃ as a function of thefrequency modulating the tunable bus versus time, in accordance with anembodiment of the present invention. Regions where population in qubitQ₃ decreases correspond to the difference in frequency (energy) betweenthe excited energy levels. The plot shows the difference in energy (orfrequency) between the excited energy level |0100> of qubit Q₃ andenergy levels |0001> of qubit Q₁, between the excited energy level|0100> of qubit Q₃ and energy level |0010> of qubit Q₂, and between theexcited energy level |0100> of qubit Q₃ and energy level |1000> of qubitQ₄ is, respectively, 873 MHz, 793 MHZ and 751 MHz. The plot shows thatthe interaction is stable over at least a time frame of 5 μs and givestypical timescales for the interaction (less than about 1 μs).

FIG. 5B is a plot of the energy or frequency difference of the firstexcited energy levels of the four qubits Q₁, Q₂, Q₃ and Q₄, according toan embodiment of the present invention. The three lower horizontal linesin the plot that are below about 200 MHZ correspond to transitionsbetween the three states |0001>, |0010> and |1000> of qubits Q₁, Q₂ andQ₄. These three are located within a relatively narrower bandwidth ofenergies or frequencies. The term “narrower” is used herein to mean thatthe bandwidth (about 122 MHz in this case) is smaller than thedifference in energy (around 800 MHz) between the energy states of eachof three qubits and the fourth qubit. The three upper horizontal linesin the plot that are between about 750 MHz and about 900 MHz correspondto the excitation manifold that includes the excited energy level |0100>of qubit Q₃. Transitions out of the qubit space (e.g., a transitionbetween state |1001> and state |0002>), lie between the lower horizontallines and the upper horizontal lines in the plot. This plot demonstratesthat the tunable bus interaction is not sufficient on its own becausetransitions between similar frequency qubits are within the samebandwidth as transitions out of the qubit subspace.

Returning to FIG. 3 , the quantum computing device 30 further includes asecond plurality of qubits 38 having the second resonance frequency anda third qubit 40 having the first resonance frequency. The quantumcomputing device 30 further includes a second tunable frequency bus 42configured to couple the third qubit 40 to the second plurality ofqubits 38. In an embodiment, the second plurality of qubits 38 includethe second qubit 34.

In an embodiment, the second plurality of qubits 38 are configured tointeract with each other through the second tunable frequency bus 42 viacross-resonance (CR). In an embodiment, the third qubit 40 and thesecond plurality of qubits 38 are configured to interact through thesecond tunable frequency bus 42 (via parametric iSWAP gate). In anembodiment, the third qubit 40 is prevented from interacting viacross-resonance with the first plurality of qubits 32.

In an embodiment, the quantum computing device 30 further includes asecond plurality of qubits 38 having the second resonance frequency anda third qubit 40 having a third resonance frequency. In this embodiment,the third resonance frequency is different from the first resonancefrequency of the first plurality of qubits 32 and from the secondresonance frequency of the second plurality of qubits 38. The secondtunable frequency bus 42 is configured to couple the third qubit 40 tothe second plurality of qubits 38. In an embodiment, the secondplurality of qubits 38 are configured to interact with each otherthrough the second tunable frequency bus 42 via cross-resonance (CR). Inan embodiment, the third qubit 40 and the second plurality of qubits 38are configured to interact through the second tunable frequency bus 42via a parametric iSWAP gate.

In an embodiment, the second plurality of qubits 38 comprise threequbits. The three qubits are configured to interact with each otherthrough the second tunable frequency bus 42 via cross-resonance (CR),and the third qubit 40 is configured to interact with the three qubits38 through the second tunable frequency bus 42 via a parametric iSWAPgate.

As it can be appreciated from the above paragraphs there is alsoprovided a method of producing a quantum computing device (e.g., thequantum computing device 10), according to an embodiment of the presentinvention. The method includes producing a first plurality of qubits 12having a first resonance frequency and a second qubit 14 having a secondresonance frequency on a qubit chip (for example as shown FIG. 4C). Thesecond frequency is different from the first frequency. The methodfurther includes at least one of producing a first fixed frequency bus16 on the qubit chip or attaching the qubit chip to a chip comprisingthe first fixed frequency bus 16 so as to enable interaction between thefirst plurality of qubits 12 via cross-resonance (CR). The method alsoincludes at least one of producing a first tunable frequency bus 18 onthe qubit chip or attaching the qubit chip to a chip comprising thefirst tunable frequency bus 18 so as to enable coupling at least one ofthe first plurality of qubits 12 to the second qubit 14 using the firsttunable frequency bus 18.

According to an embodiment of the present invention, as it can beappreciated from the above paragraphs, there is further provided amethod of producing a quantum computing device (for example, quantumcomputing device 30). The method includes producing a first plurality ofqubits 32 having a first resonance frequency and a second qubit 34having a second resonance frequency on a qubit chip (for example thequbit chip shown in FIG. 4C). The second frequency is different from thefirst frequency. The method also includes at least one of producing afirst tunable frequency bus 36 on the qubit chip or attaching the qubitchip to a chip comprising the first tunable frequency bus 36 so as toenable coupling at least one of the first plurality of qubits 32 to thesecond qubit 34 using the first tunable frequency bus 36.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

We claim:
 1. A quantum computing device, comprising: a plurality ofqubits having respective resonance frequencies, wherein at least twoqubits of the plurality of qubits have different resonance frequencies;and a plurality of frequency buses configured to couple the plurality ofqubits; and wherein pairs of adjacent qubits of the plurality of qubitshaving a same resonance frequency are only coupled via cross-resonance,and pairs of adjacent qubits of the plurality of qubits having differentresonance frequencies are only coupled via respective parametric iSWAPgates, and wherein each pair of adjacent qubits of the plurality ofqubits does not have an intervening qubit on an associated frequency busconnecting the pair of adjacent qubits.
 2. The quantum computing deviceof claim 1, wherein at least one frequency bus of the plurality offrequency buses is a fixed frequency bus.
 3. The quantum computingdevice of claim 2, wherein the fixed frequency bus is configured tocouple a pair of the pairs of adjacent qubits via cross-resonance. 4.The quantum computing device of claim 1, wherein at least one frequencybus of the plurality of frequency buses is a tunable frequency bus. 5.The quantum computing device of claim 4, wherein the tunable frequencybus is configured to couple a pair of the pairs of adjacent qubits viacross-resonance.
 6. The quantum computing device of claim 4, wherein thetunable frequency bus comprises a superconducting quantum interferencedevice.
 7. The quantum computing device of claim 1, wherein theplurality of qubits are arranged in columns and rows.
 8. The quantumcomputing device of claim 7, wherein the columns of the qubits arecoupled via respective frequency buses of a subset of the plurality offrequency buses.
 9. The quantum computing device of claim 7, wherein therows of the qubits are coupled via respective frequency buses of asubset of the plurality of frequency buses.
 10. The quantum computingdevice of claim 7, wherein subsets of the qubits are coupled viarespective frequency buses of the plurality of frequency buses.
 11. Amethod of producing a quantum computing device comprising: producing aplurality of qubits having respective resonance frequencies, wherein atleast two qubits of the plurality of qubits have different resonancefrequencies; and producing a plurality of frequency buses configured tocouple the plurality of qubits; and wherein pairs of adjacent qubits ofthe plurality of qubits having a same resonance frequency are configuredto only be coupled via cross-resonance, and pairs of adjacent qubits ofthe plurality of qubits having different resonance frequencies areconfigured to only be coupled via respective parametric iSWAP gates, andwherein each pair of adjacent qubits of the plurality of qubits does nothave an intervening qubit on an associated frequency bus connecting thepair of adjacent qubits.
 12. The method of claim 11, wherein theproducing the plurality of frequency buses comprises producing a fixedfrequency bus.
 13. The method of claim 12, configuring the fixedfrequency bus to couple a pair of the pairs of adjacent qubits viacross-resonance.
 14. The method of claim 11, wherein the producing theplurality of frequency buses comprises producing a tunable frequencybus.
 15. The method of claim 14, wherein the producing the tunablefrequency bus comprises configuring the tunable frequency bus to couplea pair of the pairs of adjacent qubits via cross-resonance.
 16. Themethod of claim 14, wherein the producing the tunable frequency buscomprises producing the tunable frequency bus comprising asuperconducting quantum interference device.
 17. The quantum computingdevice of claim 11, wherein the producing the plurality of qubitscomprises arranging the plurality of qubits in columns and rows.
 18. Thequantum computing device of claim 17, wherein the producing theplurality of frequency buses comprises coupling columns of the qubitsvia respective frequency buses of a subset of the plurality of frequencybuses.
 19. The quantum computing device of claim 17, wherein theproducing the plurality of frequency buses comprises coupling rows ofthe qubits via respective frequency buses of a subset of the pluralityof frequency buses.
 20. The quantum computing device of claim 17,wherein the producing the plurality of frequency buses comprisescoupling subsets of the qubits via respective frequency buses of theplurality of frequency buses.